Featured Dataset
Data for “Learning transitions of topological surface codes”
# Zenodo repository for the paper "Learning transitions of topological surface codes" # ### Abstract: ### For the surface code, topological quantum order allows one to encode logical quantum information in a ro-
File Size414.6 MB
Data TypeDataset
Published2025
Licensecc-by-4.0
Total Views175
Total Downloads16
# Zenodo repository for the paper “Learning transitions of topological surface codes” #
### Abstract: ###
For the surface code, topological quantum order allows one to encode logical quantum information in a ro-
bust, long-range entangled many-body quantum state. However, if an observer probes this quantum state by
performing measurements on the underlying qubits, thereby collecting an ensemble of highly correlated clas-
sical snapshots, two closely related questions arise: (i) do measurements decohere the topological order of the
quantum state; and (ii) how much of the logical information can one learn from the snapshots? Here we address
these questions for measurements in a uniform basis on all qubits. We find that for generic measurement an-
gles, sufficiently far away from the Clifford X, Y, and Z directions (such as the X+Y +Z basis) the logical
information is never lost in one of the following two ways: (i) for weak measurement, the topological order
is absolutely robust; (ii) for projective measurement, the quantum state inevitably collapses, but the logical
quantum information is faithfully transferred from the quantum system to the observer in the form of a tomo-
graphically complete classical shadow. At these generic measurement angles and in the projective-measurement
limit, the measurement ensemble enforced by Born probabilities can be represented by a 2D tensor network
that can be fermionized into a disordered, free-fermion network model in symmetry class DIII, which gives
rise to a Majorana “metal” phase. When the measurement angle is biased towards the X or Z limits, a critical
angle indicates the threshold of a learning transition beyond which the classical shadow no longer reveals full
tomographic information (but reduces to a measurement of the logical X or Z state). This learning transition
can be described in the language of the network model as a “metal to insulator” transition. For the anisotropic
“insulating” angles, there is also a finite learnability threshold in terms of the measurement strength, above
which the surface code breaks down. In terms of universality, this latter transition is generically a Nishimori
transition. Our results can be generalized from qubit measurement to syndrome measurement, demonstrating
that – in the presence of coherent errors – even syndrome measurements can enable the observer to learn the
logical information and collapse the topological order across a learnability threshold.
## Repository structure ##
This repository is structured into three subfolders.
All numerical data is
📤 Share this page
Found this useful? Share it with your network.
Files are hosted on the source repository. Click download to access the full dataset.
Han, Bo (2025). Data for “Learning transitions of topological surface codes”. https://doi.org/10.5281/zenodo.18001896